@article{MTMT:34781671,
	title = {The resolution of three exponential Diophantine equations in several variables},
	url = {https://m2.mtmt.hu/api/publication/34781671},
	author = {Bertók, Csanád and Hajdu, Lajos},
	doi = {10.1016/j.jnt.2024.01.009},
	journal-iso = {J NUMBER THEORY},
	journal = {JOURNAL OF NUMBER THEORY},
	volume = {260},
	unique-id = {34781671},
	issn = {0022-314X},
	year = {2024},
	eissn = {1096-1658},
	pages = {29-40}
}

@article{MTMT:34399660,
	title = {Terms of recurrence sequences in the solution sets of norm form equations},
	url = {https://m2.mtmt.hu/api/publication/34399660},
	author = {Hajdu, Lajos and Sebestyén, Péter},
	doi = {10.1007/s00013-023-01941-3},
	journal-iso = {ARCH MATH},
	journal = {ARCHIV DER MATHEMATIK},
	volume = {122},
	unique-id = {34399660},
	issn = {0003-889X},
	abstract = {The structure as well as several arithmetic properties of the solution sets of norm form equations are of classical and recent interest. In this paper, we give a finiteness result for terms of linear recurrence sequences appearing in the coordinates of solutions of norm form equations. Our main theorem yields a common generalization of certain recent results from the literature.},
	year = {2024},
	eissn = {1420-8938},
	pages = {179-187}
}

@article{MTMT:34244476,
	title = {Error Correction for Discrete Tomography},
	url = {https://m2.mtmt.hu/api/publication/34244476},
	author = {Ceko, Matthew and Hajdu, Lajos and Tijdeman, Rob},
	doi = {10.3233/FI-222154},
	journal-iso = {FUND INFOR},
	journal = {FUNDAMENTA INFORMATICAE},
	volume = {189},
	unique-id = {34244476},
	issn = {0169-2968},
	abstract = {Discrete tomography focuses on the reconstruction of functions from their line sums in a finite number d of directions. In this paper we consider functions f : A -> R where A is a finite subset of Z(2) and R an integral domain. Several reconstruction methods have been introduced in the literature. Recently Ceko, Pagani and Tijdeman developed a fast method to reconstruct a function with the same line sums as f. Up to here we assumed that the line sums are exact. Some authors have developed methods to recover the function f under suitable conditions by using the redundancy of data. In this paper we investigate the case where a small number of line sums are incorrect as may happen when discrete tomography is applied for data storage or transmission. We show how less than d/2 errors can be corrected and that this bound is the best possible. Moreover, we prove that if it is known that the line sums in k given directions are correct, then the line sums in every other direction can be corrected provided that the number of wrong line sums in that direction is less than k/2.},
	keywords = {error correction; Polynomial-time algorithm; Discrete Tomography; Vandermonde determinant; line sums},
	year = {2023},
	eissn = {1875-8681},
	pages = {91-112}
}

@article{MTMT:34069923,
	title = {On polynomials with only rational roots},
	url = {https://m2.mtmt.hu/api/publication/34069923},
	author = {Hajdu, Lajos and Tijdeman, Robert and Varga, Nóra},
	doi = {10.1112/mtk.12209},
	journal-iso = {MATHEMATIKA},
	journal = {MATHEMATIKA},
	volume = {69},
	unique-id = {34069923},
	issn = {0025-5793},
	abstract = {In this paper, we study upper bounds for the degrees of polynomials with only rational roots. First, we assume that the coefficients are bounded. In the second theorem, we suppose that the primes 2 and 3 do not divide any coefficient. The third theorem concerns the case that all coefficients are composed of primes from a fixed finite set.},
	year = {2023},
	eissn = {2041-7942},
	pages = {867-878},
	orcid-numbers = {Varga, Nóra/0000-0003-0489-9255}
}

@article{MTMT:33843349,
	title = {Additive Diophantine Equations with Binary Recurrences, S-Units and Several Factorials},
	url = {https://m2.mtmt.hu/api/publication/33843349},
	author = {Bérczes, Attila and Hajdu, Lajos and Luca, Florian and Pink, István},
	doi = {10.1007/s00025-023-01871-0},
	journal-iso = {RES MATHEM},
	journal = {RESULTS IN MATHEMATICS},
	volume = {78},
	unique-id = {33843349},
	issn = {1422-6383},
	abstract = {There are many results in the literature concerning linear combinations of factorials among terms of linear recurrence sequences. Recently, Grossman and Luca provided effective bounds for such terms of binary recurrence sequences. In this paper we show that under certain conditions, even the greatest prime divisor of u(n) - a(1)m(1)! - . . . - a(k)m(k)! tends to infinity, in an effective way. We give some applications of this result, as well.},
	keywords = {Baker's method; Binary recurrence sequence; Greatest prime factor},
	year = {2023},
	eissn = {1420-9012}
}

@article{MTMT:33841313,
	title = {The Diophantine equation $f(x)=g(y)$ for polynomials with simple rational roots},
	url = {https://m2.mtmt.hu/api/publication/33841313},
	author = {Hajdu, Lajos and Tijdeman, R.},
	doi = {10.1112/jlms.12746},
	journal-iso = {J LOND MATH SOC},
	journal = {JOURNAL OF THE LONDON MATHEMATICAL SOCIETY},
	volume = {108},
	unique-id = {33841313},
	issn = {0024-6107},
	abstract = {In this paper we consider Diophantine equations of the form f(x)=g(y)$f(x)=g(y)$ where f$f$ has simple rational roots and g$g$ has rational coefficients. We give strict conditions for the cases where the equation has infinitely many solutions in rationals with a bounded denominator. We give examples illustrating that the given conditions are necessary. It turns out that such equations with infinitely many solutions are strongly related to Prouhet-Tarry-Escott tuples. In the special, but important case when g$g$ has only simple rational roots as well, we can give a simpler statement. Also we provide an application to equal products with terms belonging to blocks of consecutive integers of bounded length. The latter theorem is related to problems and results of Erdos and Turk, and of Erdos and Graham.},
	year = {2023},
	eissn = {1469-7750},
	pages = {309-339}
}

@article{MTMT:33704865,
	title = {Diophantine equations for Littlewood polynomials},
	url = {https://m2.mtmt.hu/api/publication/33704865},
	author = {Hajdu, Lajos and Tijdeman, Robert and Varga, Nóra},
	doi = {10.4064/aa220912-3-11},
	journal-iso = {ACTA ARITH},
	journal = {ACTA ARITHMETICA},
	volume = {210},
	unique-id = {33704865},
	issn = {0065-1036},
	year = {2023},
	eissn = {1730-6264},
	pages = {223-234},
	orcid-numbers = {Varga, Nóra/0000-0003-0489-9255}
}

@article{MTMT:33025271,
	title = {Extrema of polynomials with real roots and Diophantine equations},
	url = {https://m2.mtmt.hu/api/publication/33025271},
	author = {Hajdu, Lajos and Herendi, Orsolya},
	doi = {10.1016/j.jnt.2022.05.004},
	journal-iso = {J NUMBER THEORY},
	journal = {JOURNAL OF NUMBER THEORY},
	volume = {242},
	unique-id = {33025271},
	issn = {0022-314X},
	keywords = {polynomial values; Extrema of polynomials with real roots},
	year = {2023},
	eissn = {1096-1658},
	pages = {626-646}
}

@article{MTMT:32844207,
	title = {On additive and multiplicative decompositions of sets of integers composed from a given set of primes, II (multiplicative decompositions)},
	url = {https://m2.mtmt.hu/api/publication/32844207},
	author = {Győry, Kálmán and Hajdu, Lajos and Sárközy, András},
	doi = {10.4064/aa220805-13-6},
	journal-iso = {ACTA ARITH},
	journal = {ACTA ARITHMETICA},
	volume = {210},
	unique-id = {32844207},
	issn = {0065-1036},
	year = {2023},
	eissn = {1730-6264},
	pages = {191-204},
	orcid-numbers = {Sárközy, András/0000-0003-0156-4601}
}

@article{MTMT:33158512,
	title = {Uniform bounds for the number of powers in arithmetic progressions},
	url = {https://m2.mtmt.hu/api/publication/33158512},
	author = {Hajdu, Lajos and Papp, Ágoston},
	doi = {10.1007/s13398-022-01313-6},
	journal-iso = {RACSAM REV R ACAD A},
	journal = {REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS},
	volume = {116},
	unique-id = {33158512},
	issn = {1578-7303},
	abstract = {We give sharp, in some sense uniform bounds for the number of l-th powers and arbitrary powers among the first N terms of an arithmetic progression, for N large enough.},
	keywords = {POWERS; Arithmetic progressions; l-th powers},
	year = {2022},
	eissn = {1579-1505}
}